Past Events

We give power saving asymptotics for \sum_{x,y<X} d(x^4+y^4). This constitutes the first case of estimates for a divisor sums along such a sparse sequence breaching the hyperbola method since 1963 work of Hooley for single variable quadratics. The techniques involve a mix of algebraic number…

Heegaard Floer homology was originally defined over the integers by Ozsvath and Szabo using choices of coherent orientations on the moduli spaces. In this talk I will explain how to construct orientations in a more canonical way, by using a coupled Spin structure on the Lagrangian tori. This…

Contact homeomorphisms are points in the closure of the (compactly supported) contactomorphism group in the homeomorphism group under the C^0-topology. Recently, Dimitroglou Rizell and Sullivan showed that the images of closed Legendrians under contact homeomorphisms are…

In joint work with Diederik van Engelenburg, Romain Panis and Franco Severo, we study the probability that the origin is connected to the boundary of the box of size n (the one-arm probability) in several percolation models related to the Ising model. We prove that different universality classes…

Let E(epsilon) be the set of all complex numbers whose real part is within distance epsilon of an integer. The pyjama problem asks if, for every positive epsilon, finitely many rotations of E(epsilon) can cover the entire complex plane. This was answered affirmatively by Manners in…

Abstract: Over the past year, Aristotle, a new system combining formal methods and language modeling, has achieved gold-medal level performance at the IMO, solved open conjectures, and opened up a strange new way of working with math. This talk will explain the technology behind Aristotle and…

We give a combinatorial description of link Floer homology. Then, we outline the Manolescu-Sarkar construction for the link Floer stable homotopy type, and give the two ways in which it extends over the full grid. We find both resulting Steenrod squares, and give an example where one of them is…

The moduli space of rank n local systems on a Riemann surface S famously admits "cluster coordinates," which are now part of the "higher Teichmuller theory" of Fock and Goncharov. It was later discovered by Gaiotto, Moore, and Neitzke that these coordinate charts can be identified with the…